<p> Golden ratio min/max </p>

1980a15e-30d5-4911-85a4-a94b7268233d 19 4 5 decimal

&[DATE] &[TIME] - &[FILENAME]

respective coefficients of heat absorbption ... °C/min ? b.water 0.1403 : b.air 0.0175 : 12 mat

0.1403

0.05

0 °C * °F 32

T.i 150 : T.∞ 40 : 12 mat

starting datum °C B T.i T.∞ - (T.∞ + : 150

t.water 0.01 ln b.water / - : 32.8237

t.air 0.01 ln b.air / - : 263.1526

°C 1 :

t 0 min * (201 range :

t T.water e b.water - (t *^B * :

t T.air e b.air - (t *^B * :

t U t t T.water vectorize t T.air vectorize augment :

t U 11 mat °C 01501501 130.36 147.4 2 113.3 144.84 3 98.47 142.33 4 85.58 139.86 5 74.38 137.43 6 64.64 135.05 7 56.18 132.71 8 48.82 130.4 9 42.43 128.14 10 36.88 125.92 11 32.05 123.73 12 27.86 121.59 13 24.21 119.48 14 21.04 117.41 15 18.29 115.37 16 15.89 113.37 17 13.81 111.4 1812 109.47 19 10.43 107.57 20 9.07 105.7 213 mat 11 mat

time 't' min u 64 :

header min water air 13 mat :

Observer u u T.water u T.air augment :

User header t U stack :

Observer 64 0.0189 48.942 13 mat

Ob min °C Water °C Air 13 mat Observer stack (:

relative temperature [°C] evolution over time [min]

x T.water x T.air 0 B + 50 black 1 5 mat u 0 + 200 black 1 5 mat 4 1 sys

User min water air 01501501 130.36 147.4 2 113.3 144.84 3 98.47 142.33 4 85.58 139.86 5 74.38 137.43 6 64.64 135.05 7 56.18 132.71 8 48.82 130.4 9 42.43 128.14 10 36.88 125.92 11 32.05 123.73 12 27.86 121.59 13 24.21 119.48 14 21.04 117.41 15 18.29 115.37 16 15.89 113.37 17 13.81 111.4 1812 109.47 19 10.43 107.57 20 9.07 105.7 223 mat

Ob min °C Water °C Air 64 0.0189 48.942 23 mat

min °C °C 13 mat

<p> Golden ratio min/max </p>

Code adapted from Valery Ochov Mathcad 11 f a b test TOL Extrema a b G 32 / b * 12 / a * - 12 / 5 sqrt * a b - (* + : y1 y2 ≥ (max in range ≡ y1 y2 ≤ (min in range ≡ x1 a b G eval : y1 x1 f eval : x2 b a G eval : y2 x2 f eval : 41 line iter 0 : iter 1000 < a b - abs TOL ≤ break test b x2 : x2 x1 : y2 y1 : x1 a b G eval : y1 x1 f eval : 51 line a x1 : x1 x2 : y1 y2 : x2 b a G eval : y2 x2 f eval : 51 line if iter iter 1 + : 21 line if while a b + 2 / 71 line :

a b + 2 / iter 21 mat

x f x T.water x T.air - (B + 11 line :

. . . as interpreted, , , i.e: Unary system

1. Unit volume of water = Unit volume of air

2. Both @ B °C @ rest conditions & sea level pressure.

3. By magic suddently subjected to new 0 °C

4. Imaginative min time evolution wrt unary volume.

5. Unsourced . . . b.water & b.air

6. Unsourced . . . T.water(t) & T.air(t)

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y1 y2 ≥ (max in range ≡ y1 y2 ≤ (min in range ≡ 21 sys

ε 109 -^:

X f 0128 y1 y2 ≤ ε Extrema :

X 16.951

X f 52.4108

Differential °C change vs time evolution ...

x f 0 B + 40 red 1 5 mat X X f + 40 red 1 5 mat 128 B 384 B 2 2 mat 4 1 sys